The total cosmic SFR density is an important tool to constrain the evolution of galaxies. It has been measured robustly below \(z\)  = 2–3, where multiwavelength data (especially in the far-IR) are available. At higher redshifts, the evolution of the SFR density is more uncertain due to the lack of far-IR data to measure the total SFR and to include dust-obscured galaxies.
[1]} derives the first robust measurement of the total cosmic SFR density at \(z=\)  4–6 based on UV\(+\) ALMA multiwavelength data from ALPINE. The detailed procedure of this measurement is described in the respective paper. In brief, the total SFR density is obtained by integrating over the full SFR function, which was derived from two different proxy density distribution functions: the absolute UV (\(M_{\rm UV}\) ) LF and the stellar mass function. The total SFR density is then obtained by integration from 0.03–100 \({\rm L_{*}}\)  or \(\log (M/{M}_{\odot })\)  = 6.0–12.4.
The right panel in Figure REF  shows the resulting SFR density function derived for the ALPINE galaxies (red symbols). The red boxes show the derived SFR density from serendipitous far-IR detections from [2]}. The green box shows the SFR density when including an overdensity of serendipitously detected C\(^+\)  emitters [3]}. The ALPINE measurements are slightly higher than the prediction from Illustris TNG [4]} and measurements from [5]}, but in line with the measurements from [6]}. The contribution of galaxies to the dust-obscured SFR density from the MORA \(2\,{\rm mm}\) 
survey [7]} are also shown.
